Abstract
The paper discusses an extension of the variance-gamma process with stochastic linear drift coefficient. It is assumed that the linear drift coefficient may switch to a different value at the exponentially distributed time. The size of the drift jump is supposed to have a multinomial distribution. We have obtained the distribution function, the probability density function and the lower partial expectation for the considered process in closed forms. The results are applied to the calculation of the value at risk and the expected shortfall of the investment portfolio in the related multivariate stochastic model.
Highlights
The variance-gamma distribution determines a well-known model of the financial data evolution
The paper discusses an extension of the variance-gamma process with stochastic linear drift coefficient
If we suggest that the drift coefficient might change, the usual choice for its time modeling is the exponential distribution
Summary
The variance-gamma distribution determines a well-known model of the financial data evolution. A number of modern research papers confirms statistically the idea to use the variance-gamma distribution for the financial index modeling by the statistical analysis of the stock market data. Luciano and Schoutens (2016) model the S&P500, the Nikkei225 and the Eurostoxx financial indices by the variance-gamma process. Luciano et al (2016); Wallmeier and Diethelm (2012) confirm the use of the variance-gamma distribution for the modeling of the US and the Swiss stock markets, respectively. Göncü et al (2016) show that the variance-gamma model fits well with the financial data of developed markets. Hoyyi et al (2021) argue for the use of the variance-gamma distribution for the return modeling on the Southeast Asian stock markets Göncü et al (2016) show that the variance-gamma model fits well with the financial data of developed markets. Hoyyi et al (2021) argue for the use of the variance-gamma distribution for the return modeling on the Southeast Asian stock markets
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